1. Field of Invention
The present invention relates to well logging using gamma ray spectroscopy. More particularly, the invention concerns a method for evaluating the penetration of materials such as proppant, casing annulus fill, or packed gravel by radioactively tagging the material, generating data signals by detecting gamma rays emitted by the tagged material, and applying an improved low-noise processing routine to the data signals to determine the tagged material's diameter.
2. Description of Related Art
"Hydraulic fracturing" is a well-known technique for increasing the amount of oil produced in an oil well. In hydraulic fracturing operations, a viscous "fracturing" fluid is forced down a cased, perforated oil well at high pressures. Fluids, such as crude oil, acid, water, or a variety of gelled liquids are typically used as fracturing fluids. The fracturing fluid exits the well through perforations in the casing, and then creates fissures or enters existing fissures in the strata adjacent to the well. The pressure applied to the fluid is increased until formation breakdown occurs, whereupon the fissures surrounding the oil well widen considerably. Injection is continued with a "proppant", which typically comprises a slurry of a selected grade of sand or gravel or particles of other material, such as alumina. After the hydraulic pressure is released, the proppant remains behind to "prop" the fracture open. The proppant may comprise a material such as sand, bauxite, ceramic, or another granular material. The fracturing fluid typically dissipates into the surrounding strata and the proppant provides a high-permeability path for the oil to reach the borehole.
In hydraulic well fracturing operations, it is important to know how far the fracturing fluid or the proppant has penetrated into the formation, radially outward from the borehole. Such information can be used for optimizing future fracturing operations in other wells in the vicinity, or for diagnosing post-stimulation problems. For example, if the fluid does not travel a sufficient distance into the strata away from the borehole, the resulting fractures may be inadequate in length to drain the reservoir of hydrocarbons to the extent desired. A similar problem occurs if the proppant fails to extend adequately into the fractures. In some cases, the proppant may "sand up" near or inside the borehole, rather than advancing into the outlying fractures, necessitating expensive removal operations.
In "gravel packing" operations, like hydraulic fracturing operations, it is important to understand the distribution of certain materials about the cased borehole. Gravel packing operations are performed in cased boreholes where there is a need to regulate the flow of hydrocarbon fluids into the well through the casing. One reason to regulate the fluid flow, for example, might be to achieve an optimal flow rate to more completely and efficiently drain the hydrocarbon reserves. In some gravel packing operations, material such as gravel is "pre-packed" through perforations in the well casing, adjacent to the regions of high fluid flow. This material is ultimately deposited in outlying volumes surrounding the casing, thereby restricting the flow of formation solids into the borehole with the hydrocarbon fluids.
In gravel packing operations, like hydraulic well fracturing procedures, it is important to know how far the gravel has penetrated into the formation. It is also useful to understand the extent of gravel placement between the gravel pack screen and the casing. If the gravel failed to adequately penetrate and fill the cavities surrounding the casing, the gravel may not restrict the pressure of solids to the extent desired.
Measurement of the distribution of certain materials about a cased borehole is also important in "annulus fill operations." Annulus fill operations involve placing a filler such as cement between the well casing and the borehole to secure the casing in place and to seal off formation strata, thereby preventing undesired formation fluids from leaking into the borehole. In annulus fill operations, it is often useful to analyze and understand the distribution of the filler about the well casing.
In hydraulic well fracturing, gravel packing, and annulus fill operations, radioactive tracers are commonly used to tag the fluid, proppant, gravel, or filler. Each of these radioactive tracers contains a material that emits a known spectrum of gamma rays. Typical tracers are Scandium (.sup.46 Sc), Antimony (.sup.124 Sb), or Iridium (.sup.192 Ir). After attempting to distribute one or more tagged materials, well site personnel conduct a gamma ray well log to measure and record the gamma ray energy distribution emanating from the radioactive tracer(s) as a function of depth. This permits petroleum engineers or geophysicists to estimate the distribution of the tracer(s), and hence the fluid, proppant, or filler.
For many years, radioactive tracers have been used to measure the distribution of materials about a borehole. Early techniques determined the location of a tagged material by conducting logging measurements with a "gross-counting" gamma ray tool, such as a Geiger counter. Although gross-counting tools are sensitive to the overall presence of gamma rays, they are not responsive to the individual gamma ray energy signatures characteristic of different tracers. Therefore, although gross-counting tools have been useful for some applications, their usefulness is limited in other applications since they are only sensitive to overall vertical variations of the tracers.
More recently, though, scientists have learned that gamma ray spectroscopy tools are helpful in measuring the distribution of downhole materials, and especially beneficial in overcoming the limitations of gross-counting tools. Even for a single tracer, the observed gamma ray energy spectrum contains information about the radial distribution of the tagged material surrounding the borehole. For instance, known gamma ray spectroscopy techniques are sometimes used to determine whether a tagged material has been deposited in the borehole, or whether it has been disposed of beyond the casing as desired. Gamma ray spectroscopy is also beneficial since it can be used to detect two or more tracer isotopes with distinct gamma ray signatures. This is often beneficial, for example, in complex fracturing operations where multiple zones are fractured or where fracturing fluids are injected in several stages. In these situations, it may be desirable to inject and monitor multiple tracers in the fracturing operations.
Multiple-tracer operations may be implemented in a number of different ways. For example, different radioactive isotopes may be injected into different zones, or at different stages of the operation. Or, different radioactive isotopes may be used to tag different components of the fracturing material. For example, one isotope may be used to tag the fracturing fluid with another isotope being used to tag the proppant. By monitoring each of these radioactive tracer isotopes, scientists can more accurately understand the effectiveness of the fracturing operation, especially in determining the depth, extent, and radial location of the fractures. Moreover, witch multiple tracers, a single logging pass is often sufficient to identify the individual tracers and provide sufficient raw data to evaluate the effectiveness of the job.
To glean as much information as possible from gamma ray spectroscopy, scientists have developed more and more sophisticated analysis techniques. Many early multiple tracer operations used a spectrum-stripping method, as discussed in Gadeken & Smith, "TracerScan, A Spectroscopy Technique for Determining the Distribution of Multiple Radioactive Tracers in Downhole Operations," The Log Analyst (January-February 1987), pp. 27-36.
The spectrum-stripping method was later improved with a weighted least squares analysis, based in part upon laboratory tests performed under simulated field conditions. The weighted least squares analysis helped geophysicists to achieve tracer logs that were more accurate and less statistical.
Along these lines, one especially useful technique for performing gamma ray well logging is disclosed in U.S. Pat. No. 4,825,073 ('073), entitled "Method for Determining Depth of Penetration of Radioactive Tracers in Formation Fractures," which issued to Smith, Jr. et al. on Apr. 25, 1989. The '073 patent is hereby incorporated herein by reference in its entirety. The '073 patent is concerned with measuring a tracer's penetration from the borehole (i.e., its "relative distance") as a function of depth.
As explored by Smith, Jr. et al., the gamma ray energy spectra for formation 100, cement annulus 102, and borehole 104 portions of a tracer-tagged operation can be measured separately in the laboratory to generate individual "basis spectra" (FIG. 1A). The principal scattering mechanism of gamma rays of low energies (e.g. 0.2-2.0 Mev) is the "Compton effect," where the Compton-scattered part of a gamma ray spectrum contains information about the distance gamma rays travel between emission and detection. These phenomena, as explored by Smith, Jr. et al., are useful in measuring a tracer's relative distance from the detector. In this respect, the borehole gamma rays 104 are least affected by Compton scattering and the formation gamma rays 100 are most affected by Compton scattering. This is true since gamma rays that travel from the formation into the borehole necessarily pass through, and are potentially scattered by, more atoms of the intervening material during that journey.
To determine a tracer's relative distance, the tracer's "Compton Ratio" is first measured, where Compton Ratio refers to a count rate in a specified high-energy portion of the spectrum divided by a count rate in a specified low-energy portion of the spectrum, where the effects of Compton scattering will predominate. After determining the tracer's Compton Ratio, the relationship between the tracer's relative distance and that tracer's Compton Ratio is established. Then, this relationship is applied to a gamma ray log for a given depth to provide a relative distance log for the depth range. This process is addressed in detail in the '073 patent, as well as Gadeken et al., "Calibration and Analysis of Borehole and Formation Sensitivities for Gamma Ray Spectroscopy Measurements with Multiple Radioactive Tracers," presented at 28th Annual SPWLA Symposium, London, England (1987).
More particularly, the technique of Smith, Jr. et al. employs a weighted least squares technique to process data obtained from the gamma ray log. The weighted least squares technique assumes that only "borehole" and "formation" regions contain tagged materials. The borehole region is used to refer to the region inside the borehole, and the formation region is used to refer to the region outside the cement annulus. For each isotope, the weighted least squares process calculates the borehole and formation components. The total detected isotope concentration may be obtained by summing the borehole and formation components.
It has been established that other tracer distributions may be accurately approximated by a linear combination of the borehole and formation components yielded by the weighted least squares analysis. For example, FIG. 1B illustrates the similarity between the cement annulus spectrum 102 and a composite spectrum 150 generated by summing 39% of the borehole spectrum 104 with 61% of the formation spectrum 100. The borehole and formation percentages were obtained as output from the weighted least squares procedure when the measured annulus spectrum was used as the input. This demonstrates that a composite spectrum is a close estimate of the actual gamma ray spectrum for a specific isotope that is actually in an intermediate annular location. This illustrates the usefulness of the "basis spectra" approach in this implementation of the weighted least squares process.
An appropriate composite spectrum is presumably a close estimate of the actual gamma ray spectrum for a specific isotope. Using an appropriate composite spectrum, a Compton Ratio is computed by summing the gamma ray counts in high energy region (e.g. 350 keV to 3000 keV), and dividing that quantity by the sum of gamma ray counts in a low energy region (e.g. 150 keV to 350 keV). The resulting Compton Ratio calculation is inversely proportional to the square of the annular diameter of a cylindrical region containing the tracer isotope, as taught in the '073 patent. This estimate of annular diameter, called "relative distance", is proportional to the mean radial distance between the measuring tool and the tracer material. Compton Ratio techniques are addressed in Gadeken & Smith, "A Relative Distance Indicator from Gamma Ray Spectroscopy Measurements with Radioactive Tracers," SPE 17962 (1989), as well as the "Calibration and Analysis of Borehole and Formation Sensitivities . . . " paper identified above. These papers are hereby incorporated by reference in their entirety.
The use of analysis techniques based on Compton Ratio calculations provides a great deal of beneficial information for users in the applications such as the foregoing. However, due to the details of the implementation of the Compton Ratio technique, the results are not entirely satisfactory, due to a number of reasons.
One potential problem with Compton Ratio techniques concerns the interpretation of data. Generally, the matrix inversion of the weighted least squares process rarely exhibits instability or singularity characteristics. This means that negative borehole and/or formation components will not usually disturb the computations. However, interpreting negative components may be a problem in some situations. Basically, a negative formation component indicates that the specified tracer isotope is closer to the tool than occurred in the laboratory, i.e. uniformly tagged water inside a cased borehole. Similarly, a negative borehole component means that the isotope is more distant from the tool than occurred in the laboratory conditions (i.e. a uniformly distributed tracer in a cylindrical annulus from the cement column to the outer limit of the tool response).
Thus, a negative borehole component may indicate an inner annular diameter that is greater than the outer diameter of the cement column. If both borehole and formation components are negative, however, a physical interpretation is not possible. This situation arises most often when multiple isotopes are used (e.g. 2-3 isotopes), due to statistical variations or data transmission infidelities.
The linear relation between Compton ratio and radial distance, is shown in Equation 1 (below). EQU R.sub.c =A+B/d.sup.2 [ 1]
where:
R.sub.c =Compton Ratio, PA1 A=a constant that depends on the specific isotope and the measurement geometry, PA1 B=a constant that depends on the specific isotope and the measurement geometry, and PA1 d=relative distance.
The relationship of Equation 1, however, is only truly accurate for a specific annular geometry. Specifically, the constants A and B are determined for each different casing size. Once the constants A and B are established for a particular model, the relationship of Equation 1 will still be generally true in actual field conditions. However, since the actual downhole geometry may be unknown, and since the tracer distribution may be different than that of the laboratory, the values of the constants A and B may be inaccurate in the field. This condition therefore requires an interpretation analyst to manipulate A and B to ensure that Equation 1 yields reasonable estimates of relative distance.
Additionally, the construction of the composite spectrum for each isotope is subject to statistical variations. This results in rather significant variations of the Compton Ratio from the relative distance calibration measurements. For example, negative values of the Compton Ratio can be observed for some individual isotopes, especially where more than two isotopes have been used.
Moreover, Compton Ratio methods may not be entirely satisfactory in some applications due to the level of noise in the relative distance log. Noise is inherent in the nature of the processes resulting in the emission and detection of gamma ray photons. However, it is exacerbated by the division of one count rate by another in the Compton Ratio technique.
Known Compton Ratio methods, then, are not as useful as required, since such methods often require especially accurate, and intuitive log interpretation techniques. In addition, Compton Ratio techniques can be time consuming especially when multiple isotopes are used, because several iterations with different values of A and B may be necessary to obtain a valid log interpretation. Furthermore, Compton Ratio techniques may not be as accurate as desired due to the influence of noise.